What is (x-5)^2-(y+1)^2=2 ?

The solution to (x-5)^2-(y+1)^2=2 is Hyperbola with (h,k)=(5,-1),a=sqrt(2),b=sqrt(2)

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(x-5)^2-(y+1)^2=2

(x - 5)^{2} - (y + 1)^{2} = 2

(h, k) = (5, - 1), a = 2, b = 2

Solution steps

(x - 5)^{2} - (y + 1)^{2} = 2

Rewrite

(x - 5)^{2} - (y + 1)^{2} = 2

in the form of a standard hyperbola equation

\frac{( x - 5 ) ^{2}}{( 2 ) ^{2}} - \frac{( y - ( - 1 ) ) ^{2}}{( 2 ) ^{2}} = 1

Therefore Hyperbola properties are:

(h, k) = (5, - 1), a = 2, b = 2

9 y^{2} - 25 x^{2} - 100 x - 108 y - 1 = 0

\frac{x ^{2}}{6} - \frac{y ^{2}}{25} = 1

x^{2} - y^{2} + 4 = 0

4 x^{2} - y^{2} - 16 x + 2 y + 3 = 0

\frac{x ^{2}}{9} - \frac{y ^{2}}{9} = 1

What is (x-5)^2-(y+1)^2=2 ?
The solution to (x-5)^2-(y+1)^2=2 is Hyperbola with (h,k)=(5,-1),a=sqrt(2),b=sqrt(2)